Argumentation-based abduction in disjunctive logic programming

Abstract

In this paper, we propose an argumentation-based semantic framework, called DAS, for disjunctive logic programming. The basic idea is to translate a disjunctive logic program into an argumentation-theoretic framework. One unique feature of our proposed framework is to consider the disjunctions of negative literals as possible assumptions so as to represent incomplete information. In our framework, three semantics preferred disjunctive hypothesis (PDH), complete disjunctive hypothesis (CDH) and well-founded disjunctive hypothesis (WFDH) are defined by three kinds of acceptable hypotheses to represent credulous, moderate and skeptical reasoning in artificial intelligence (AI), respectively. Furthermore, our semantic framework can be extended to a wider class than that of disjunctive programs (called bi-disjunctive logic programs). In addition to being a first serious attempt in establishing an argumentation-theoretic framework for disjunctive logic programming, DAS integrates and naturally extends many key semantics, such as the minimal models, extended generalized closed world assumption (EGCWA), the well-founded model, and the disjunctive stable models. In particular, novel and interesting argumentation-theoretic characterizations of the EGCWA and the disjunctive stable semantics are shown. Thus the framework presented in this paper does not only provide a new way of performing argumentation (abduction) in disjunctive deductive databases, but also is a simple, intuitive and unifying semantic framework for disjunctive logic programming.